I've owned a Flash game website since late January. The name isn't a dictionary word, though it ends in "gaming". The domain is a .net domain. Recently, the .com version of that domain dropped, and a competitor picked it up and redirects it to their own site. Searching the name in Google brings up the recently acquired .com first, with the .net bumped down to second result. The site doesn't make more than $80 a month, so it isn't huge, but my traffic has dropped significantly since I lost first place in Google for the site's name. Needless to say, the other site is probably gaining from this. Do I have any sort of case, or is this my fault for not grabbing the .com when it dropped?
With good seo work and keywords you can compete with the .com domain. It is not true that always a .com domain win.
Possibly you can contact and buy the .COM domain from the person who bought it, and make a deal. If s/he refuses, try investing in SEO.
Owning a domain give you no trademark rights. Usage in commerce can establish a common law trademark in some cases - this depends on whether the name is eligible for trademark protection and whether or not you were the first person to use, and continue to use, the mark for a certain class (type of usage). From a practical standpoint, it would be much cheaper to pay for the domain than take legal action. Filing a WIPO action will cost you about $4k and the decision isn't binding if the person wants to take it to court. Court fees would easily run well over $10,000 and into six figures through the entire court process. Appeals would add considerably to this amount. If you can purchase the domain for under a couple of thousand, I would do it. If they still don't want to sell, see an intellectual property rights attorney if you are prepared to spend a lot in legal fees.
You have no automatic rights to a word just because you have a domain with that name or word in it. If you rank second in Google, too bad for you, but good domaining from the other party. That's just how the internet work. Learn and adapt. Then go do some SEO work and win back that first place.
do not worry about .com and concentrate on building quality backlinks to your site. I have a .info domain which shows on first 10 in google and other tlds with my domain shows on 5+ pages.